Answer:
1st question:
10°, 80°, 90°
2nd question:
76°, 52°, 52°
Explanation:
For both of these questions we will use the idea that the three angles of a triangle add up to 180°.
In the triangle on the left, two angles are marked and the third is a right angle. The tiny square marking on the third angle means it is a right angle, so it is 90°.
We can write an equation.
x + 8x + 90° = 180°
combine like terms
9x + 90 = 180
subtract 90
9x = 90
divide by 9
x = 10
So the angles are x, 8x and 90°
Since x = 10
the 3 angles are 10°, 80° and 90°
For the second question, two sides are marked to show they are congruent (same, equal) that means the two angles on the base (base angles) are congruent (the same)
One angle is 3x+1 and both the other two angles are 2x+2. Write an equation.
3x+1 + 2x+2 + 2x+2 = 180°
combine like terms
7x + 5 = 180
subtract 5
7x = 175
divide by 7
x = 25
Calculate the angle measures using x = 25
3x+1 = 3(25)+1 = 76°
2x+2 = 2(25)+2 = 52°
The 3 angles of the triangle are 76°, 52° and 52°